The diagram shows a circle with the centre O. A, B and C lie on the circumference of the circle. Work out

∠AOB=112°

Step-by-step explanation:

Then in our case ∠AOB -central ; ∠ACB= inscribed  

Then :

let ∠AOB=2∠ACB=2α ; ∠ACB=α

Then :

∠COA+∠COB+2α=360 (because the full angle is O)

∠СOA+∠COB=360-2α  

And we know :

∠СOA+∠COB+∠CAO+∠ACB+∠CBO=360

360-2α+α+∠CAO+∠CBO=360  

360-a=360-∠CAO-∠CBO

Then :

α=(32+24)=56°  ; ∠AOB=2α=56*2=112°

r and t.

both are 64 degrees.